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%I A066319 #48 Sep 08 2022 08:45:04
%S A066319 1,1,6,96,3000,155520,12101040,1321205760,192849310080,36288000000000,
%T A066319 8556520581100800,2471543044256563200,858447696200353459200,
%U A066319 353034171594345598156800,169665960401437500000000000
%N A066319 A labeled structure simultaneously a tree and a cycle.
%D A066319 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 68 (2.1.37).
%H A066319 G. C. Greubel, <a href="/A066319/b066319.txt">Table of n, a(n) for n = 1..230</a>
%H A066319 D. E. Knuth, <a href="https://doi.org/10.1090/S0002-9939-1989-0949878-9">A recurrence related to trees</a>, Proc. Amer. Math. Soc. 105 (1989), 335-349. Reprinted as Chapter 39 of Selected Papers on Discrete Mathematics by D. E. Knuth.
%H A066319 Thorsten Weist, <a href="https://arxiv.org/abs/1203.2740">On the Euler characteristic of Kronecker moduli spaces</a>, arXiv preprint arXiv:1203.2740 [math.RT], 2012. Cor. 5.3, k=1. But offset 0.
%H A066319 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A066319 a(n) = n^(n-2)*(n-1)!.
%t A066319 Table[n!*n^(n-3), {n,1,20}] (* _G. C. Greubel_, May 29 2019 *)
%o A066319 (PARI) a(n) = n^(n-2)*(n-1)!; \\ _Michel Marcus_, May 29 2019
%o A066319 (Magma) [n^(n-3)*Factorial(n): n in [1..20]]; // _G. C. Greubel_, May 29 2019
%o A066319 (Sage) [n^(n-3)*factorial(n) for n in (1..20)] # _G. C. Greubel_, May 29 2019
%K A066319 nonn
%O A066319 1,3
%A A066319 _Christian G. Bower_, Dec 13 2001
%E A066319 Knuth reference from _David Callan_, Feb 07 2004

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